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Introduction E9F5FC
Questions FFFFC0
Software
Life, Statistics, Biology discovery
Understand knowledge and ignorance in terms of the concept of information as relevant in mathematics, computer science and physics.
- What is the definition of information?
- How are information and entropy related?
- How are information and communication related?
- How does information relate to the levels of knowledge in the foursome?
- How does information entropy relate to a 1x1 random matrix and an nxn random matrix and their eigenvalues?
Information
- The resolution of uncertainty (ambiguity, symmetry).
- Symmetry breaking.
- A bridge from nondeterminism to determinism.
- The reversal of irreversability. Thus related to the duality of body and mind.
- Quantifies as {$S=k_{B}\textrm{ln}\Omega$} the number {$\Omega$} of microscopic configurations (microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Here we assume that each microstate is equally probable.
- Expresses the number of possible solutions to a given set of constraints.
- Expresses the ambiguity in the possible explanations of the given situation.
- Expresses the degree of irreversibility.
- Shannon entropy of a random variable: {$H=-\sum_{i}p_i \textrm{log}_2(p_i)$}. The average level of uncertainty-surprise-information in the variable's possible outcomes. The average amount of information contributed by the variable.
Tendency towards maximum entropy
Constructor theory
- https://en.wikipedia.org/wiki/Constructor_theory
- https://gizmodo.com/a-meta-theory-of-physics-could-explain-life-the-univer-1844806293
Information is what you learn. What you learn grows at the boundary, has the shape of the boundary. A shape can be thought of as being created by integrating over these boundaries as they increase.
Gregory Chaitin = Shannon + Turing = Compression-Decompression as understanding.
Information capacity is zero if probability is the same for all cases but also if one case is given 100%. Information transmission requires asymmetry. Otherwise you cannot define choice.
Probability
- Kleisli categories and probability - 01 - The Giry monad
- Giry monad related to probability.
Quantum computing
- https://en.wikipedia.org/wiki/Probabilistic_programming
- probabilistic programming paradigm (quantum computing)
- Measurement based quantum computer vs gate based quantum computer
- lattice surgery
- https://en.wikipedia.org/wiki/Toric_code Quantum error correcting code
- topological quantum computer
- https://en.wikipedia.org/wiki/One-way_quantum_computer
- The Geometry of Semidefinite Programming
https://en.wikipedia.org/wiki/Koopman%E2%80%93von_Neumann_classical_mechanics
https://www.amazon.com/Quantum-Challenge-Foundations-Mechanics-Astronomy/dp/076372470X
In what sense are Feynman diagrams relativistic given that they have directions for time and for space?
Instead of thinking of speed of light, think of a clock that doesn't tick, so that t=0 always. And this is the case for the quantum harmonic osciallator and for the particle-clocks with no steps